In General > s.a. quantum-gravity phenomenology; special relativity [including anisotropy of the speed of light].
* Motivation for tests: An observed violation would be a manifestation of quantum-gravity effects.
* Possibilities: Small shifts of an atom's energy levels, detectable in atomic clocks (& Kostelecký); Deviations of cross sections and reaction thresholds from standard model predictions (note that Lorentz violation is sometimes associated with CPT violation); Modified dispersion relations measurable in time-of-flight experiments, including faster than light travel; Anisotropies in the speed of light, testable with rotating resonators; Vacuum birefringence; Would be associated with a violation of the equivalence principle.
* 2001: In analysis of cosmological sources, the coefficients for Lorentz violation are bounded by 3 × 10³².
* 2004: Preferred frame models are for all practical purposes ruled out by experimental bounds (& Sudarsky).
* 2006: Lower bound of 0.0066 E_P ~ 0.66 × 10¹⁷ GeV on violation scale from GRB 051221A; No effect on electron spin down to 10⁻²¹ eV from University of Washington torsion-balance experiment [@ news pn(06)apr].
* 2007: Michelson-Morley experiments give bounds of order 10⁻¹⁶ on coefficients for electrons and photons.
* 2009: No anisotropy in light propagation has been seen at the 10⁻¹⁷ level.
* 2012: Explicit Lorentz-invariance breaking is very tightly constrained by experiment, and deformations generically lead to problems with locality.
* 2014: Michelson-Morley experiments give bounds of order 10⁻¹⁸ on coefficients for electrons and photons.
* 2015: Tight bound >1.6 E_P (99% c.l.) for energy scale of stochastic fluctuations in photon propagation speed.
@ General references: Amelino-Camelia NJP(04); Allen & Yokoo NPPS(04)ht [terrestrial + space based experiments]; Pospelov & Pomalis PT(04)jul; Kostelecký SA(04)sep, a0802-conf; Mattingly LRR(05)gq; Bailey & Kostelecký PRD(06) [framework]; Liberati PoS-a0706; Kostelecký & Russell RMP(11)-a0801-conf [data tables, updated 2010]; Mattingly a0802-conf [proposals]; Kostelecký & Mewes ApJ(08)-a0809 [with electromagnetic waves, framework]; Bluhm a1302-ch [standard model extension, overview]; Liberati CQG(13)-a1304 [rev]; Bailey a1505-conf, a1906-conf [rev]; Accioly et al a1604 [photon gravitational deflection].
> Related topics: see modified lorentz group; tests of general relativity with light [light bending]; violations of lorentz symmetry.

Earth-Based Tests > s.a. Anisotropy; diffraction; Ether [drift].
@ Interferometry: Lämmerzahl CQG(98)gq; Amelino-Camelia & Lämmerzahl CQG(04)gq/03; Müller et al PRL(08) [Mach-Zehnder atom interferometer and isotropy of gravity]; Pruttivarasin et al Nat(15)jan-a1412 [Michelson-Morley experiment for electrons]; Nagel et al nComm(15)-a1412 [precision tests]; > s.a. Michelson-Morley Experiment.
@ Gravitational-wave interferometers: Hansen et al PRD(15)-a1412; Melissinos a1601-wd; Kostelecký & Mewes PLB(16)-a1602; Schreck CQG(17)-a1603.
@ Resonators: Lipa et al PRL(03) + pn(03)feb; Stanwix et al PRL(05)hp, PRD(06)gq [microwave]; Müller PRD(05); Herrmann et al PRL(05), PRD(09); Müller et al PRL(07); Eisele et al PRL(09) + news pw(09)sep [no isotropy violation at the 10⁻¹⁷ level]; Baynes et al PRD(11) [non-rotating odd-parity asymmetric optical resonator]; Michimura et al PRL(13)-a1303 [optical ring cavity].
@ Hydrogenlike atoms: Belich et al PRD(06)ht; Kharlanov & Zhukovsky JMP(07)-a0705; de Campos Borges & Barone Rangel EPJC(16)-a1601 [corrections to the the ground state energy and wave function].
@ Atomic physics: Bluhm hp/01-conf, et al PRL(99), et al PRL(02)hp/01 [clocks]; Russell PS(05) [and optical]; Hohensee et al PRL(13)-a1303 [dysprosium]; Pihan-Le Bars et al a1701 [atomic clocks]; Shaniv et al PRL(18)-a1712; Sanner et al a1809 [optical clocks]; news cosmos(19)mar [atomic clocks].
@ Bose-Einstein condensates: Visser et al ht/01-conf; Colladay & McDonald PRD(06); Casana & da Silva MPLA(15)-a1106 [ideal bosonic gas].
@ Beta decay: Noordmans et al PRL(13) [reanalysis of old experiments on forbidden decays]; Díaz et al PRD(13)-a1305 [bounds on coefficients].
@ Other experiments: Wolf et al PRL(03), GRG(04)gq, PRD(04)hp [oscillator and maser]; Kholmetskii PS(03) [Mössbauer spectroscopy]; Tobar et al PRD(05)hp/04 [photons, scalar + parity-odd coefficients]; Canè et al PRL(04) [neutrons, bounds on boost effects]; Cardone et al FP(06) [DC voltage produced by constant B field]; Kostelecký & Tasson PRL(09)-a0810 + news ns(09apr [gravity-matter coupling]; Altschul PRD(10) [electron, boosts], PRD(10)-a1005 [electron]; Bennett et al a1008-conf [tests of gravity]; DeAngelis et al NCC-a1011-proc [bound on asymmetry of particle lifetimes]; Noordmans & Vos PRD(14) [charged-pion decay]; Lo et al PRX(16)-a1412 [using rotating quartz oscillators]; Abe et Super-Kamiokande PRL(15) [with atmospheric neutrinos, no signs of violations]; Long & Kostelecký PRD(15)-a1412, Kostelecký & Mewes PLB(17)-a1611 [in short-range gravity, tungsten oscillators]; Shao et al PRL(16)-a1607 [submillimeter scale]; Kislat & Krawczynski PRD(17)-a1701; Tizchang et al EPJC(19)-a1811 [laser beam interacting with charged lepton beam]; Escobar & Martín-Ruiz PRD(19)-a1902 [ultracold neutrons].
@ And the equivalence principle: Halprin & Kim PLB(99); > s.a. classical equivalence principle.
@ And constants: Kostelecký et al PRD(03)ap/02.

Space-Based and Astrophysical Tests > s.a. topological defects.
* Binary pulsars: Violations of Lorentz symmetry in the orbital evolution of binary pulsars would induce a much more rapid decay of their orbital periods due to the emission of dipolar radiation.
@ Space-based: Bluhm et al PRD(03) [and CPT]; Battat et al PRL(07)-a0710 [lunar laser ranging]; Klioner et al a1002 [astrometry]; Overduin et al a1307-conf [constraints from Gravity Probe B]; Hees et al PRD(15)-a1508 [with planetary orbital dynamics]; Bourgoin et al PRL(16)-a1607, a1706 [lunar laser ranging]; Pihan-le Bars et al PRL(19)-a1912 [MICROSCOPE space mission].
@ Using gamma-ray bursts: Rodriguez & Piran JCAP(06)ap, et al JCAP(06); Xiao & Ma PRD(09)-a0909; Maccione et al PRL(10)-a1003 [in stringy spacetime models]; Stecker APP(11)-a1102 [polarization, absence of birefringence]; Ellis & Mavromatos APP(13)-a1111 [and AGNs]; Kostelecký & Mewes PRL(13)-a1301 [improved sensitivity using GRB linear polarization]; Otte et al a1305-conf [prospects]; Vasileiou et al PRD(13)-a1305; Couturier et al a1308-proc; Zhang & Ma APP(14)-a1406; Vasileiou et al et al nPhys(15)mar + news pw(15)mar [bound on energy scale for photon speed fuzziness]; Pan et al ApJ(15)-a1505 [Markov chain Monte Carlo approach, no evidence]; Wei et al ApJ(17)-a1704 [constraints from GRB 160625B]; Acciari et MAGIC PRL(20) [constraints from GRB 190114C]; > s.a. gamma-ray astronomy and GRBs; phenomenology of lorentz violation.
@ Very-high-energy photons: Rubtsov et al PRD(14)-a1312 [detection]; Daniel et al a1508-proc [Cherenkov Telescope Array].
@ Using neutrinos: Biesiada & Piórkowska JCAP(07)-a0712 [neutrino tof delays]; Guo et al PRD(12)-a1206 [cmb data and the neutrino sector]; Amelino-Camelia et al a1307 [using IceCube data]; Ellis et al a1807 [multimessenger observations of blazar TXS 0506+056].
@ Using pulsars: Jacobson et al Nat(03)ap/02 [Crab nebula synchrotron radiation]; Maccione et al JCAP(07)-a0707 [Crab nebula and dispersion relations]; Altschul PRD(07)hp/06 [neutrons and pulsar timing]; Xie RAA(13)-a1208 [binary pulsars and constraints on standard model extension]; Otte a1208-proc [VHE emission from pulsars]; Shao & Wex CQG(12)-a1209 [small-eccentricity binary pulsars]; Shao et al a1211-MG13, Shao et al CQG(13)-a1307; Yagi et al PRL(14)-a1307 [binary pulsars]; Shao PRL(14)-a1402, PRD(14)-a1412 [and standard-model extension]; Jennings et al PRD(15)-a1510 [binary pulsars].
@ Using gravitational waves: Sotiriou PRL(18)-a1709 [from black-hole binaries]; Mewes PRD(19)-a1905.
@ Other astrophysics: Bailey a0709-conf; Biesiada & Piórkowska MNRAS(09)-a0712 [lensing delays]; Altschul PRD(08) [for pions]; Jacob & Piran PRD(08)-a0810 [extragalactic gamma-ray sources]; Tso & Bailey PRD(11) [light bending]; Boncioli et al a1509-conf [UHE cosmic rays]; Lorentz & Brun a1606-proc [blazar Mrk 501 flare]; Bettoni et al JCAP(17)-a1702 [using satellite galaxies]; Nogués et al PoS-a1710 [combined studies].

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